Mathematical Methods of Physics

Dr Judith A McGovern

Who should take this course?

This course is core for third year Physics with Theoretical Physics students, and may be taken by other third and fourth year Physics students (but not Maths/Physics) who have been following the theory courses. Familiarity with Mathematics of Waves and Fields, and with some of the material of Lagrangian Mechanics, Complex Variables and Vector Spaces, Electrodynamics and Mathematical Fundamentals of Quantum Mechanics, will be assumed.

The subject of the course is well described by the title; it covers a variety of mathematical methods that are generally useful for physicists. Some, such as properties and methods of solutions of differential equations, will build on familiar material but go into more depth; others, such as integral equations, are likely to be new.

This course is not a specific prerequisite for any other course, but Green's functions (propagators) are used extensively in Quantum Field Theory.

The syllabus is given in the UG handbook entry for the course. The main course site is on Blackboard.

Textbooks and websites

The primary textbooks for this course are Arfken, Weber and Harris, Mathematical Methods for the Physical Sciences (7th edition) and Riley, Hobson and Bence, Mathematical Methods for the Physics and Engineering (3rd edition). The former has changed substantially in organisation from the 6th edition.

As an extra resource, you may be interested in these notes created by previous lectures of the course. The material of the first two chapters is covered these days in Mathematics of Waves and Fields, Complex Variables and Vector spaces, and in Mathematical Fundamentals of Quantum Mechanics, so not all of the material will be covered in this course.

Lecture notes


You are encouraged to explore numerical solutions and exploit Mathematica's algebraic skills. If you prefer to use another programme, you may still wish to download the Wolfram CDF Player which will enable you to view the files below. Mathematica is installed in the PC clusters, too; furthermore Wolfram Alpha allows limited web-based facilities.